How to fetch all photos from library

The code shown below is what i've tried already.What I wish to achieve is to fetch all the photos from the device.Currently only a few are being fetched.How to modify the code so as to load all the images from device?

let fetchOptions = PHFetchOptions()

let collection:PHFetchResult = PHAssetCollection.fetchAssetCollectionsWithType(.Moment, subtype: .Any, options: fetchOptions)

if let first_Obj:AnyObject = collection.firstObject
{
    self.assetCollection = first_Obj as! PHAssetCollection
}

Updated David's answer for iOS 10+ & Swift 4.x/3.x:

Request permission from the device to access photos:

Add the following value to your info.plist

Privacy - Photo Library Usage Description

And provide a string that is shown to the user.

Request all images:

PHPhotoLibrary.requestAuthorization { status in
    switch status {
    case .authorized:
        let fetchOptions = PHFetchOptions()
        let allPhotos = PHAsset.fetchAssets(with: .image, options: fetchOptions)
        print("Found \(allPhotos.count) assets")
    case .denied, .restricted:
        print("Not allowed")
    case .notDetermined:
        // Should not see this when requesting
        print("Not determined yet")
    }
}